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The Greatest And The Luckiest Of Mortals
sgant writes "So says the 18th-century French mathematician Joseph-Louis Lagrange about Sir Isaac Newton. The New York Times has a piece on 'The Newtonian Moment: Science and the Making of Modern Culture' which is a new exhibit at the NY Public Library. It includes a number of Newton's manuscripts from the Cambridge University Library, including a first edition of his most famous work, "Principia," bearing the author's corrections and additions for the next printing, have never before been shown in the United States."
not invented, discovered
also, Leibniz also independantly devised the system of calculus at the same time
I know Lucas isn't the most popular round here at the moment, but I still like this line by Sir Alec Guiness: "In my experience, there's no such thing as luck"
Iran has endorsed
That was Leibnitz, you insensitive clod!
(and thus, the science's oldest flame war is brought into the 21st century!)
It's said that he died a virgin... so in at least one respect Newton was not, and did not get, "lucky".
Well, Archimedes discovered quite a few calculus-esque ideas such as adding up infinite slices to determine the area of something in a cube. This was of course quite some time ago. Although these different calculuses (calculii) vary quite a bit I think that some credit should also go to Archimedes.
( o ) one could say I'm rather baked
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I'm enduring college level calculus right now, and to think that one man, more or less invented a major area of mathematics that we use in a vast array of situations, is simply, incredible.
Boy is that ever true, I remember when going through all my calc classes that I found it hard to conceive that someone could ever figure out all this stuff on their own. It's hard enough to remember/learn even now (unless you're really talened at math) after hundreds of years and countless refinement.It's not just Newton though. I had to take a math history class as part of my "capstone" courses to get my CS degree. It was a fascinating course and we learned of so many people who developed different areas of math. One thing I remember well because it was funny is that pretty much everyone who's done significant work on set theory has spent time in mental hospitals, most after they did the work. :)
And of course, Archimedes pretty much a cat's whisker away from discovering the integral around 200 BC, as described in the nearly lost work "The Method"
Newton didn't get it 'wrong' it is just that his theories are less accurate at extremes - Einstein's theories of relativity produce answers that are the same as Newton's theories of motion at 'non-relativistic' speeds (hence the term non-relativistic).
These speeds (or more properly velocities perhaps) are those anything less than a significant fraction of the speed of light (or very close to a massive object for gravitational calculations). So, you only need Newton's equations for almost all practical applications.
He did not "invent" or "discover" the thing by himself. It's like all research: people put brick after brick, and then someone puts the last one and says "here is a building", and gets all the credit. And many years later (30 for Albert, 300 for Isaac) some geeks put posters of the guy in their rooms and suddenly feel illuminated. :)
"Plague is sweeping across England, and a young Isaac Newton retreats to the isolation of Lincolnshire. Sitting in the family garden he watches an apple fall, and unlocks the secrets of gravity - or does he? Adam explores the truth behind this famous moment in the history of science, and discovers that Newton wrote his own account over forty years after the supposed event."
Listen to it here (starts 1 min 50 secs in)
I went to the same boys school as Newton originally went to, called the 'Kings School' in Grantham, Lincolnshire, England where Newton scratched his name into the wall of the old library. As was the custom at the time, many other students scratched and carved their names. His looks considerably less impressive than others. We were all taught that he attended the school and about his subsequent accomplishments. There is a garden named after him with a single apple tree in the middle, although it's not one he ever sat under. One of the various 'houses' in the school is also named after him. The town has a statue of him in front of the guildhall (equivalent to a town hall). However, in their rush to name things after him they have named a travisty of a shopping mall after him, which is awful, it's called the 'Isaac Newton Shopping Centre' and is particularlly down market with a big plastic apple hanging high near one of the entrances. Growing up asa kid I saw Newton's name and face everywhere as he adorned the back of the one pound note, the equivalent of a $1 bill. Sadly that was replaced by a coin with nobody on the reverse of the queens 'head' side. Even worse my home town is now remembered more for 'Maggie Thatcher' than Newton. I hope that one day the place will be associated more for Newton than Thatcher, but it is unlikely as he wasn't born there (he was born in Colsterworth nearby), only attending school there for a while when he was young. Lastly, I hope that Apple Computer bring back their Newton as it was a fantastic machine which deserved to bear the name of such an amazing man.
I'm enduring college level calculus right now, and to think that one man, more or less invented a major area of mathematics that we use in a vast array of situations, is simply, incredible.
That's because they don't teach it the way it was developed. What you learn is a santised version and you learn it in the wrong order (compared to order of discovery and development).
These posts express my own personal views, not those of my employer
While some of Newtons ideas were later proven to be incorrect by Einstein
Without the imperfect (but functional) model developed by Newton (which we still use today with some refinements! very few situations require a more complex model of forces and effects) it seems unlikley that Einstein would have been able to develop relativity, indeed many other advances would not have been made until someone else replicated Newton's work.
Newton himself said "If I have seen further, it is because I stand on the shoulders of giants" (which is etched onto the Brish pound coin) - and he is definatly one of the giants upon which later physists stood. Science is a process, not a product, and viewing it in terms of right and wrong is foolish - it's a series of advances leading to a more and more accurate understanding of the universe. No step towards that goal is any less worthy than another.
Beep beep.
To learn it the other way around, as mentioned above, pick up Tom Apostol's Calculus (2 vols).
Newton himself said of his work that he was only "standing on the shoulders of giants" meaning that if he had discovered new knowledge, it was from the ideas put down by euclid, archimedes etc before him.
(This phrase is engraved round the edge of £2 coins in the UK, since Newton also invented milling the edges of coins to prevent people from clipping them.)
However, he was probably being too modest. It wasn't just calc: this guy basically went away at some point in his life and came up with:
His laws of motion, which explained pretty much every physical phenomenom then studied.
His theory of gravity, which relates the movement of celestial bodies back to the laws of motion.
and
The differential calculus, which provided the maths necessary to apply all this.
He also did work in optics and other fields, and invented the catflap.
If anyone surpasses him as a physicist, it must be Einstein.
If anyone surpasses him both as a physicist and a mathematician, it's news to me.
Respect is due.
my password really is 'stinkypants'
The story about him and Robert Hooke is quite and interesting one and makes you think about how much he actually did do. Robert Hooke did infact accuse Newton of plagiarism but the charge was dropped because Hooke didn't have proof of his own theory and made some assumptions on intuitive grounds.
Makes one think that if someone would now proof Einsteins theory of relativity, if they would then discredit Einstein for the discovery.
Keep in mind that calculus as we know it has been modified somewhat from their original formulation. For instance, both Newton and Leibinitz incorrectly used infintesimals in their definitions. It wasn't until the 1800's that Karl Weierstrass formulated the limit definition that we use today.
The darkness... controls the music. The music... controls the soul.
It's pretty well known that Einstein didn't come up with relativity on his own. The equations and some of the analysis had already been done by Lorentz. Unfortunately Lorentz didn't want to fully accept the conclusions and he had a far narrower view of the effects. Einstein came along and formulated a diffrent derrivation of all the formulas and a far far wider interpretation.
The darkness... controls the music. The music... controls the soul.
I have also read that Newton's phrase "standing on the shoulders of giants" was a veiled insult to Robert Hooke, who was apparently not the tallest of people.
flossie
Write now. Defend liberty
Or, as is the case for me and most others, "if I have failed to see further, it is because giants are standing on my shoulders".
Certain aspects of calculus were developed two centuries prior to Newton in India by Madhava of Sangamagrama. This seems to be widely accepted now. A few links to Madhava and other Keralese mathematicians are also present here.
As an engineer, I frequently use Newton's laws of motion. I can't say that I have ever had the need to consider bodies travelling at a significant fraction of the speed of light in my work.
flossie
Write now. Defend liberty
That was the old view. There were some problems with their use of infinitesimals, but those problems have been cleared up more recently. The modern version of calculus via infinitesimals is known as nonstandard analysis. The landmark work on the subject is Robinson's 1966 book "Non-standard analysis".
Moreover, that sort of hen-pecking at Newton and Leibniz is not really productive. No one cares more about precision and correctness in definitions than mathematicians, and yet mathematicians still assign credit to those two.
Have you read the Principia? I have only read portions, but Newton does some pretty amazing stuff in there, besides just the use of calculus and the derivation of the inverse square law for gravity. For example, he proves that there is no closed form for elliptic integrals of a certain kind.
I do agree that Newton discovered/invented a large part of our mathematics
No he didn't! Elementary calculus may be useful but it's only a teardrop in the ocean of mathematics. Compare to Gauss who contributed to nearly everything mathematics was studying in his time and most of which is still relevant, while Newton's formulations have long since been surpassed by more modern constructions.
And Latin. We now know Latin to be a dead language. What real scientist uses Latin?
And the English system of weights and measures. He didn't even use the Metric system, or bother to convert the values!
How the great learned history critics and scientists of the future will scoff at our inaccurate decimal system, our clunky wire-based infosystems, and our use of BASIC.
We use the tools we have. The best of us modify them to fit our own needs. Every once in a while, someone comes up with a mod that everyone agrees is really cool. On that measure, Isaac Newton is the greatest hacker of all time. OK, maybe Edison was greater, or the woman who invented the stick.
I picking on your fine post (a bit unfairly, to be sure) because if someone comes up with a mod, how does that make everything that went before it "incorrect"?
sigs, as if you care.
> Pretty amazing.
/. didn't existed at that time, so he didn't waste his time like you and I do :-)
Not at all !
Votez ecolo : Chiez dans l'urne !
Amazing how Newton's status has changed. In the early 70s the Cambridge Union Society actually sold off a copy of the Principia cheap (as the guy who beat me to it gloated at me at considerable length). They wouldn't do that nowadays when virtually every Latin edition is worth a great deal of money.
Just as it's extremely difficult to spend any time in Florence without becoming aware of the Dante connection, it's quite difficult to spend time in Cambridge, England without encountering Newton. Whatever his faults - and he was clearly not an easy person to get on with - he made major contributions to optics, pure physics, chemistry, mathematics and the running of the Royal Mint. Other people around at the time did remarkable work - Hooke, Boyle, Liebniz - but Newton surpassed them al for sheer output, breadth and depth. Logically, nowadays, with a much larger and better educated population we should be throwing up lots of Newtons. Why aren't we? Is it because all the relatively easy science and maths has now been done and it takes large organisations and computing power to make any advance at all? Or is it because clever people get pulled off into business or celebrity before they really have a chance to do any work that will really endure?
Panurge has posted for the last time. Thanks for the positive moderations.
When making "top ten" lists of physics, usually Newton, Einstein and Maxwell are among the top three physicists of all time. But such lists are in general dubious; for one thing, Einstein needed the results by Newton and Maxwell to do his own work. Beside, the three worked in very different periods of time with different problems facing physics.
What makes Newton unique, is that Newton would in general make the top ten list of all time great mathematicians. Usually the top three would be Archemides, Newton and Gauss. But again, such lists should not be trusted. If you want to rate scientists, learn what they did, and make your own (subjective) rating.
There has always been people claiming Einstein was wrong, often because Einstein's theory are strange to "common sense". And it is well known that you can make any theory fit all available experimental results by making ad hoc extensions to the theory. It is worth nothing that Newton himself would probably not have liked the extensions necessary and Newton himself found parts of his own theories lacking.
This is where you are wrong. Einstein's theories are much simpler than Newton's. To make Newton's theories and Maxwell's theories fit, you need an "ether" with very strange and peculiar properties. This was the state of physics when Einstein came along. And you need to add even stranger properties to fit what has been learned since Einstein.What Einstein did was to show that you could make a nice unified theory of Newton and Maxwell and get rid of this complicated, ad hoc concept of an ether, but you would have to change your concept of time and space in the process. So, Einstein theory of relativity passes the test of Occam. Einstein's theories are much simpler mathematically and physically than any theories that try to preserve Newton's laws and still fit known experimental facts. The only price to pay, is that common sense about time and space has to be updated.
bring it on! --- JFK
but what do i know, i'm just a model.
Incorrect might not be the right word, it was not mathematically rigorous. There were instances when he treated an infintesimal as a zero and discarded it, there were instances where he treated it as a non-zero and divided it. Math is rigorous. You need a set of rules that hold in all situations. [Emphasis added]
A set of rules that hold in all situations means that there are no paradoxes.
There is nothing non-rigorous about infintesimals which behave in some cases identically with zero when added to something and in other cases behave like non-zeros when dividing two of them. What is non-rigorous and non-defensible is the attempted distinction between zero and non-zero. Not everything mathematical is a number. In fact most mathematical things are not numbers. It all has to do with functions from spaces to spaces that preserve interesting properties.
Newton's phrase "standing on the shoulders of giants" was a veiled insult to Robert Hooke...
This allegation is made almost every time Newton is mentioned on Slashdot but it has no historical basis.
As this analysis points out, when Newton uses the phrase he is refering to both Descarte and Hook. The most obvious interpretation is that he is complementing Hook by comparing him to Descarte and referring to them both as giants.
Furthermore, Hook was not especially short and in other cases where Newton engaged in scientific debate he specifically avoided what he called "oblique and glancing expressions".
There is thus every reason to suppose that when Newton said he stood on the shoulders of giants, he was acknowledging his debt to Copernicus, Kepler, Galileo, Descartes and Hook, who was at the time England's most eminent scientist.